Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

Q1.
If 2x-7xy +3y= 0 ,then the value of x:y = ?
1) 3:2 2) 2:3
3) 3:1 and 1:2 4) 5:6
5)None of these
Answer : 3:1 and 1:2
Explanation : Given, 2x-7xy +3y= 0
or 2(x/y)2-7(x/y)+ 3 = 0
So, x/y=3/1 and x/y=1/2
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Q2.
If a,b and c are real numbers such that  a-b+c <1 , a+b+c >1 and 9a+3b+c < -4, then what is the sign of 'a'?
1) + only 2) - only
3) + or - 4) Can't be said
5)None of these
Answer : - only
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Q3.
If a,b and c are the two roots of a quadratic equation such that a+b =24 and a-b = 8, the quadratic equation having a and b as its roots is ---.
1) x2+2x+8=0 2) x2-4x+8=0
3) x2-24x+128=0 4) 2x2+8x+9=0
5)None of these
Answer : x2-24x+128=0
Explanation : Given, a+b =24 and a-b = 8
So,solving from two equations,we get a =16 and b=8
Therefore,ab=16 x 8 = 128
Quadratic equations 
x2 - ( sum of roots)+ products of the roots = 0
or x2-24x+128 = 0
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Q4.
What is the value of  'P' , if the following equation has two equal roots ?
4x2 - (P-2)x + 1 = 0
1) P=6 or P=-2 2) P=4 or P=-3
3) P=6 or P=-3 4) P=4 or P=2
5)None of these
Answer : P=6 or P=-2
Explanation : Here, a=4,b= - (P-2); c=1
Given, equation  has equal roots,then D=0

b2- 4ac =0
or p2 +4 - 4p - 16 = 0
or p2- 6p +2p - 12 =0
or p(p-6) + 2(p-2) = 0
or p=6 or -2
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